Direct products of modules and the pure semisimplicity conjecture

It is shown that, if $R$ is either an Artin algebra or a commutative noetherian domain of Krull dimension $1$, then infinite direct products of $R$-modules resist direct sum decomposition as follows: If $(M_n){n \in \Bbb N}$isafamilyofnon-isomorphic,finitelygenerated,indecomposable$R$-modules,then$\prod{n\in \Bbb N} M_n$ is not a direct sum of finitely generated modules. The bearing of this direct product condition on the pure semisimplicity problem is discussed.